Systems of second-order linear ODE’s with constant coefficients and their symmetries II. The case of non-diagonal coefficient matrices |
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Authors: | R. Campoamor-Stursberg |
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Affiliation: | Dpto de Geometría y Topología, Fac. CC. Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, E-28040 Madrid, Spain |
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Abstract: | We complete the analysis of the symmetry algebra L for systems of n second-order linear ODEs with constant real coefficients, by studying the case of coefficient matrices having a non-diagonal Jordan canonical form. We also classify the Levi factor (maximal semisimple subalgebra) of L, showing that it is completely determined by the Jordan form. A universal formula for the dimension of the symmetry algebra of such systems is given. As application, the case n = 5 is analyzed. |
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Keywords: | Lie group method Point symmetry Lie algebra Levi factor Linearization |
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